Table6.KineticEquationandParametersfromReference2a

KineticEquation

reaction:oleicacid+methanolTmethyloleate+waterr)kcxAxM{1-(1/ke)[(xExW)/(xAxM)]}Ccat

activationpre-exponentialenergyheatofreactionparameter

factor(k0)(Ea;kcal/mol)( Hr;kcal/mol)

kc12.93(2.8714.00(0.99

ke

4.17(0.04

2.68(0.05a

Subscripts:A,oleicacid;M,methanol;E,methyloleate;andW,water.Units:kc(moldm3)/(gcat2min);Ccat(gcat/dm3);r(mol/(gcatmin)).

hasbeenmadebyusingasimplifiedreactormodelinwhichthekineticspreviouslydetermined2hasbeenintroduced.InTables3and4arereportedtheaverageReynoldsnumberscalculatedforeachexperimentalrun.Asitcanbeobservedthesevaluesareverylow,andintheseconditionstheflowthroughtheporousmediumisveryprobablyinthecreepingflowregime.12Inthisconditiontheplugflowmodelisnotrigorous;onthecontrary,anaxialdispersionmodelcouldbemoresuitable.Nevertheless,theroughapproximationoftheplugflowreactorhasbeenadoptedforafirsttestingofthepreviouslydeterminedkineticsinthedescriptionofthepresentexperimentaldatacollectedfortubularreactors.Ontheotherhand,Seguinetal.12haveshownamaximumrelativedeviationof10%betweenthepurelyplugflowandtheaxialdispersionmodelsincreepingflowconditions.Theuseofasimplerapproachis,therefore,justifiedasapreliminaryone,consideringboththescatteringofexperimentaldataandtheintroducedapproxima-tions.Moreover,thefluiddynamicbehaviorofacomplexsystemliketheoneusedinthisworkcontainingamixtureofspheresandspringsinthepackedbedisneverdescribedintheliterature.

Referringtoanisothermalplug-flowreactor,thedifferentialmaterialbalanceequationforeachcomponentinthesystem(excludingtriglyceridethatisaninertmedium)canbewrittenas

dFi

dW)Viri)A,M,E,W

(5)

cat

whereFiisthemolarfeedflowrateoftheithcomponent(lettersmeaningA,oleicacid;M,methanol;E,estermethyloleate;W,water),Wcatisthetotalweightofcatalystloadedinthereactor,Viisthestoichiometriccoefficientreferencedtotheithcomponent,andristhereactionrate(seeTable6forparameters,units,andotherdetails).Thenumericalintegrationofthedifferentialequationssystem5,inwhichtheexpressionforrtakenfromourpreviousworkhasbeenintroduced,2resultsincalculatedperformancesthataremuchhigherthanthoseexperimentallyobservedforthethreetubularreactors.Thismeans,inotherwords,thatthepackedbedreactorconfigurationfurnishesalowerconversionwithrespecttothatpredictedonthebasisofthekineticsexperimentallyevaluatedinabatchwellstirredslurryreactor(batchWSSR).ThisparticularbehaviorisreportedinFigure2whereacomparisonisshownbetweentheexperimentalconversionofoleicacidobtainedintherunswiththereactorTR2(squaressymbols)andtheconversionpredictedbythemodelrepresentedbyrelation5(opencirclesymbols).Theconversion,inbothcases,isreportedasafunctionoftheoverallvolumetricfeedflowrate,anditisevidentfromthediagraminFigure2thatthekinetic-basedmodelpredictsahighconversionthatispracticallyinsensitivetotheincreaseinfeedflowratetowhichcorrespondsadecrease

Ind.Eng.Chem.Res.,Vol.46,No.15,20075117

parisonbetweentheexperimentalconversionintubularreactorTR2andthepredictionofthetubularreactormodelbasedonapreviouslydevelopedkineticsfrombatchexperiments.2

inresidencetime.Theexperimentaldatareportedarerelativelyscattered,thevaluesreportedintheplotbeingtheonesobtainedinsteady-stateconditionsafteralongtimeoperation(somehours).Scatteringisduetothefluctuationoftheoperativeconditionssuchasflowrates,temperature,andanalyses.Theflowrateatwhichthemodelstartstopredictadecreaseoftheconversionofoleicacidwasestimatedatabout5000cm3/min.Inthekineticmodelthereactorperformancesarehighenoughthatthesystemreachestheequilibriumcompositionnearlyinalltherunssimulated.Excludinginthissystemtheinfluenceoftheinternaldiffusion,wehavefocusedourattentiontotheinterventionofexternalfluid-to-particlemass-transferlimita-tions.Thefollowingsectionsofthepaperarethendevotedtothefurtherdeepeningofthisaspect.

ExternalDiffusion.Withthepurelykineticmodel(eqs5)unabletocorrectlydescribetheexperimentallyobservedbehaviorofthetubularreactors,anevaluationoftheexternalliquid-soliddiffusionalresistancehasbeenmadebyadoptingthegeneralizedcriterionofMears.11Thiscriterion,referencedtoanisothermalcatalyticpelletandtoann-orderreactionrateequation,isexpressedbythefollowingrelation:

r*RpC<0.15

(6)

0ksn

whereksisthefluid-to-particlemass-transfercoefficient.This

lastparameterhasbeenestimatedinanapproximatedwaybymeansoftheCoeuretcorrelation12,13expressedbythefollowingrelation:

Sh)5.4Re1/3Sc1/4

0.04<Re<30(7)

Thisexpressionhasbeenchosen,amongthewidecorrelationsavailableintheliteratureasreportedinref12,becauseitismoresuitableintermsoflinearvelocity(seethevaluesofReynoldsnumbersreportedinthelastcolumnsofTables3and4)andparticlesizerangesofapplicability.12Thiscorrelationisveryprobablynotfullysuitableforthepackedbedsusedinourexperimentsbecauseitwasoriginallydevelopedforpackedbedsofspheres,while,asmentioned,ourpackinghasamorecomplicatedstructurebeingcomposedofbothparticlesofvarioussizeandofmetallicsprings.However,wehavedevelopedourcalculationalsowithothersimilarcorrelations